Cotoneum - Revision history

FloraC: /* Tunings */ + norm-based tunings

2026-05-22T08:51:31Z

Tunings: + norm-based tunings

@@ Line 207: / Line 207: @@
 == Tunings ==
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"
 |-
-! Edo tuning<br>(n\EDO)
+! Edo generator
-! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-Interval)]]
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
-! Generator<br>(¢)
+! Generator (¢)
 ! Comments
 |-

FloraC: /* Interval chain */ adopt CWE tuning, unify to 2 decimal places

2026-05-22T08:47:06Z

Interval chain: adopt CWE tuning, unify to 2 decimal places

Show changes

FloraC: + notation

2026-05-20T09:27:21Z

+ notation

← Older revision		Revision as of 09:27, 20 May 2026
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	<nowiki>*</nowiki> in 19-limit POTE tuning		<nowiki>*</nowiki> in 19-limit POTE tuning

	== Tuning spectrum ==		== Notation ==
			Cotoneum can be notated just like [[cassaschismic]], with accidentals for the generic comma and the generic aberschisma. As an example, we can use up and down arrows with shafts (↑/↓) for the comma step, and arrows without shafts (^/v) for the aberschisma step. The only difference is that the aberschisma step which is independent in cassaschismic is equated with the 41-comma here. In other words, we have C–^↑↑E ~ C–↓↓E, implying ~11/9 (double-comma-up minor third) + an aberschisma-up = ~27/22 (double-comma-down major third).

			== Tunings ==
			=== Tuning spectrum ===
	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|-		\|-

FloraC: Review & expand

2026-05-20T09:10:43Z

Review & expand

← Older revision		Revision as of 09:10, 20 May 2026
Line 13:		Line 13:
	\| Odd limit 2 = 21 \| Mistuning 2 = 2.48 \| Complexity 2 = 176		\| Odd limit 2 = 21 \| Mistuning 2 = 2.48 \| Complexity 2 = 176
	}}		}}
	'''Cotoneum''' is a [[rank]]-2 [[regular temperament\|temperament]] for the 7- through 19-limit~~. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]~~. The generator of cotoneum is a perfect fifth sharp by about 0.3–0.4 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found ~~at the~~ diminished fourth. Instead, 5/4 is found ~~at the~~ sextuple-diminished octave (~~–49~~ fifths). It is a weak extension of the [[2.5.7 subgroup\|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.		'''Cotoneum''' is a [[rank]]-2 [[regular temperament\|temperament]] for the 7- through 19-limit. The generator of cotoneum is a [[3/2\|perfect fifth]] sharp by about 0.3–0.4 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found as a diminished fourth. Instead, 5/4 is found as a sextuple-diminished octave (−49 fifths). It is a weak extension of the [[2.5.7 subgroup\|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]].

	It can seen as a detemperament of [[41edo\|41 equal temperament]], with the [[countercomp comma\|41-comma]] shrunk down to about ~~5-6~~ cents, ~~representing many important intervals such as~~ the [[schisma]], [[~~5120/5103~~]], [[176/175]], [[243/242]], [[~~273~~/~~272~~]], [[~~325~~/~~324~~]], [[~~352~~/~~351~~]], [[~~385~~/~~384~~]], [[~~513~~/~~512~~]], [[~~896~~/~~891~~]]~~, etc~~.		It can seen as a detemperament of [[41edo\|41 equal temperament]], with the [[countercomp comma\|41-comma]] shrunk down to about 5–6 cents for a generic aberschisma, which represents the [[schisma]] and [[aberschisma]].

			This generic aberschisma takes on more important roles from the 11-limit onwards, where it represents [[176/175]], [[243/242]], [[385/384]], [[540/539]] and [[896/891]]. In the 13-limit it represents [[352/351]], in the 17-limit [[273/272]], and in the 19-limit the undevicesimal schisma of [[513/512]].

	[[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.		[[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.

	The temperament was named by [[~~User:Xenllium\|~~Xenllium]] in 2021. ''Cotoneum'' is Latin for "quince".		The temperament was named by [[Xenllium]] in 2021. ''Cotoneum'' is Latin for "quince".

	For technical data, see [[Garischismic clan #Cotoneum]].		For technical data, see [[Garischismic clan #Cotoneum]].
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	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	! ~~Fifths~~		! #
	! Cents ~~<br>value~~*		! Cents*
	! Approximate ~~Ratios~~		! Approximate ratios
	\|-		\|-
	\| 0		\| 0

FloraC: More line breaks in the infobox to make it narrower

2026-05-20T08:03:50Z

More line breaks in the infobox to make it narrower

← Older revision		Revision as of 08:03, 20 May 2026
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	\| Title = Cotoneum		\| Title = Cotoneum
	\| Subgroups = 2.3.5.7, 2.3.5.7.11.13, 2.3.5.7.11.13.17.19		\| Subgroups = 2.3.5.7, 2.3.5.7.11.13, 2.3.5.7.11.13.17.19
	\| Comma basis = [[10976/10935]], [[823543/819200]] (7-limit);<br>[[364/363]], [[441/440]], [[3584/3575]], [[10976/10935]] (13-limit);<br>[[343/342]], [[364/363]], [[441/440]], [[595/594]], [[1216/1215]],~~<br>~~ [[1729/1728]] (19-limit)		\| Comma basis = [[10976/10935]], [[823543/819200]] (7-limit);<br>[[364/363]], [[441/440]], [[3584/3575]], <br>[[10976/10935]] (13-limit);<br>[[343/342]], [[364/363]], [[441/440]], [[595/594]], <br>[[1216/1215]], [[1729/1728]] (19-limit)
	\| Edo join 1 = 41 \| Edo join 2 = 217		\| Edo join 1 = 41 \| Edo join 2 = 217
	\| Mapping = 1; 1 -49 -14 23 61 89 -44		\| Mapping = 1; 1 -49 -14 23 61 89 -44
	\| Generators = 3/2		\| Generators = 3/2
	\| Generators tuning = 702.~~308~~		\| Generators tuning = 702.31
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[12L 17s]], [[12L 29s]], [[41L 12s]], [[41L 53s]]		\| MOS scales = [[12L 17s]], [[12L 29s]], [[41L 12s]], [[41L 53s]]

Overthink: /* Tuning spectrum */ Add edo tunings; monotone tunings; remove redundant info

2026-05-19T18:41:43Z

Tuning spectrum: Add edo tunings; monotone tunings; remove redundant info

Show changes

Overthink: fix this

2026-05-19T04:12:45Z

fix this

← Older revision		Revision as of 04:12, 19 May 2026
Line 13:		Line 13:
	\| Odd limit 2 = 21 \| Mistuning 2 = 2.48 \| Complexity 2 = 176		\| Odd limit 2 = 21 \| Mistuning 2 = 2.48 \| Complexity 2 = 176
	}}		}}
	'''Cotoneum''' is a [[rank]]-2 [[regular temperament\|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.~~4–0~~.5 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup\|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.		'''Cotoneum''' is a [[rank]]-2 [[regular temperament\|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.3–0.4 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup\|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.

	It can seen as a detemperament of [[41edo\|41 equal temperament]], with the [[countercomp comma\|41-comma]] shrunk down to about 5-6 cents, representing many important intervals such as the [[schisma]], [[5120/5103]], [[176/175]], [[243/242]], [[273/272]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], [[896/891]], etc.		It can seen as a detemperament of [[41edo\|41 equal temperament]], with the [[countercomp comma\|41-comma]] shrunk down to about 5-6 cents, representing many important intervals such as the [[schisma]], [[5120/5103]], [[176/175]], [[243/242]], [[273/272]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], [[896/891]], etc.

Overthink: slight changes

2026-05-19T01:23:31Z

slight changes

← Older revision		Revision as of 01:23, 19 May 2026
Line 15:		Line 15:
	'''Cotoneum''' is a [[rank]]-2 [[regular temperament\|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.4–0.5 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup\|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.		'''Cotoneum''' is a [[rank]]-2 [[regular temperament\|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.4–0.5 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup\|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.

	It can seen as a detemperament of [[41edo\|41 equal temperament]], with the [[countercomp comma\|41-comma]] shrunk down to about 5 cents, representing many important intervals such as the [[schisma]], [[5120/5103]], [[243/242]], [[273/272]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], [[896/891]], etc.		It can seen as a detemperament of [[41edo\|41 equal temperament]], with the [[countercomp comma\|41-comma]] shrunk down to about 5-6 cents, representing many important intervals such as the [[schisma]], [[5120/5103]], [[176/175]], [[243/242]], [[273/272]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], [[896/891]], etc.

	[[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.		[[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.
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	\| 41		\| 41
	\| 1194.618		\| 1194.618
	\| 351/176, ~~891~~/~~448~~		\| 175/88, 484/243,<br>351/176, 768/385
	\|}		\|}
	<nowiki>*</nowiki> in 19-limit POTE tuning		<nowiki>*</nowiki> in 19-limit POTE tuning

Overthink: Cut table to 41 generators. The mappings of every interval do not need to be listed.

2026-05-19T00:39:53Z

Cut table to 41 generators. The mappings of every interval do not need to be listed.

Show changes

Overthink: add a higher-limit one

2026-05-19T00:32:14Z

add a higher-limit one

← Older revision		Revision as of 00:32, 19 May 2026
Line 16:		Line 16:
	'''Cotoneum''' is a [[rank]]-2 [[regular temperament\|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.4-0.5 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup\|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.		'''Cotoneum''' is a [[rank]]-2 [[regular temperament\|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.4-0.5 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup\|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.

	It can seen as a detemperament of [[41edo\|41 equal temperament]], with the [[countercomp comma\|41-comma]] shrunk down to about 5 cents, representing important intervals such as the [[schisma]], [[5120/5103]], [[325/324]], [[352/351]], [[385/384]], [[~~540~~/~~539]], [[729/728~~]], etc.		It can seen as a detemperament of [[41edo\|41 equal temperament]], with the [[countercomp comma\|41-comma]] shrunk down to about 5 cents, representing important intervals such as the [[schisma]], [[5120/5103]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], etc.

	[[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.		[[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.